To beat the dead horse of Monty Hall’s game-show problem: Marilyn was wrong, and you were right the first time …

— Eric Dynamic, Berkeley, California

Dear Cecil:

You really blew it. As any fool can plainly see, when the game-show host opens a door you did not pick and then gives you a chance to change your pick, he is starting a new game. It makes no difference whether you stay or switch, the odds are 50-50.

— Emerson Kamarose, San Jose, California

Dear Cecil:

Suppose our task is to pick the ace of spades from a deck of cards. We select one card. The chance we got the ace of spades is 1 in 52. Now the dealer takes the remaining 51 cards. At this point his odds are 51 in 52. If he turns over 1 card which is not the ace of spades our odds are now 1 in 51, his are 50 in 51. After 50 wrong cards our odds are 1 in 2, his are 1 in 2. The idea that his odds remain 51 in 52 as more and more cards in his hand prove wrong is just plain crazy.

Give it up, gang. It was bad enough that I screwed this up. But you guys have had the benefit of my miraculously lucid explanation of the correct answer! Since you won’t listen to reason, all I can tell you is to play the game and see what happens. One writer says he played his buddy using the faulty logic in my first column and got skunked out of the price of dinner. Several other doubters wrote computer programs that, to their surprise, showed they were wrong and Marilyn vos Savant was right.

A friend of mine did suggest another way of thinking about the problem that may help clarify things. Suppose we have the three doors again, one concealing the prize. You pick door #1. Now you’re offered this choice: open door #1, or open door #2 and door #3. In the latter case you keep the prize if it’s behind either door. You’d rather have a two-in-three shot at the prize than one-in-three, wouldn’t you? If you think about it, the original problem offers you basically the same choice. Monty is saying in effect: you can keep your one door or you can have the other two doors, one of which (a non-prize door) I’ll open for you. Still don’t get it? Then at least have the sense to keep quiet about it.

Other correspondents have passed along some interesting variations on the problem. Here’s a couple from Jordan Drachman of Stanford, California: There is a card in a hat. It is either the ace of spades or the king of spades, with equal probability. You take another identical ace of spades and throw it into the hat. You then choose a card at random from the hat. You see it is an ace. What are the odds the original card in the hat was an ace? (Answer: 2/3.) There is a family with two children. You have been told this family has a daughter. What are the odds they also have a son, assuming the biological odds of having a male or female child are equal? (Answer: 2/3.)

Finally, this one from a friend. Suppose we have a lottery with 10,000 “scratch-off-the-dot” tickets. The prize: a car. Ten thousand people buy the tickets, including you. 9,998 scratch off the dots on their tickets and find the message YOU LOSE. Should you offer big money to the remaining ticketholder to exchange tickets with you? (Answer: hey, after all this drill, you figure it out.)

So I lied — This is the last you’ll ever have to read about this

Dear Cecil:

The answers to the logic questions submitted by Jordan Drachman were illogical. In the first problem he says there is an equal chance the card placed in a hat is either an ace of spades or a king of spades. An ace of spades is then added. Now a card is drawn from the hat — an ace of spades. Drachman asks what the odds are that the original card was an ace. Drawing a card does not affect the odds for the original card. They remain 1 in 2 that it was an ace, not 2 in 3 as stated.

In the second problem we are told a couple has two children, one of them a girl. Drachman then asks what the odds are the other child is a boy, assuming the biological odds of having a male or female child are equal. His answer: 2 in 3. How can the gender of one child affect the gender of another? It can’t. The answer is 1 in 2.

— Adam Martin and Anna Davlantes, Evanston, Illinois

Dear Cecil:

In a recent column you asked, “Suppose we have a lottery with 10,000 `scratch off the dot’ tickets. The prize: a car. Ten thousand people buy the tickets, including you. 9,998 scratch off the dots on their tickets and find the message `YOU LOSE.’ Should you offer big money to the remaining ticketholder to exchange tickets with you?”

If you think the answer is “yes,” you are wrong. If you think the answer is “no,” then you are intentionally misleading your readers …

— Jim Balter, Los Angeles

Cecil replies:

Do you think I could possibly screw this up twice in a row? Of course I could. But not this time. Cecil is well aware the answer to the lottery question is “no” — if there are only two tickets left, they have equal odds of being the winner. The difference between this and the Monty Hall question is that we’re assuming Monty knows where the prize is, and uses that information to select a non-prize door to open; whereas in the lottery example the fact that the first 9,998 tickets are losers is a matter of chance. I put the question at the end of a line of dissimilar questions as a goof — not very sporting, but old habits die hard.

The answers given to Jordan Drachman’s questions — 2 in 3 in both cases — were correct. The odds of the original card being an ace were 1 in 2 before it was placed in the hat. We are now trying to determine what card was actually chosen based on subsequent events. Here are the possibilities:

(1) The original card in the hat was an ace. You threw in an ace and then picked the original ace.

(2) The original card in the hat was an ace. You threw in an ace and then picked the second ace.

(3) The original card was a king; you threw in an ace. You then picked the ace.

In 2 of 3 cases, the original card was an ace. QED.

The second question is much the same. The possible gender combinations for two children are:

(1) Child A is female and Child B is male.

(2) Child A is female and Child B is female.

(3) Child A is male and Child B is female.

(4) Child A is male and Child B is male.

We know one child is female, eliminating choice #4. In 2 of the remaining 3 cases, the female child’s sibling is male. QED.

Granted the question is subtle. Consider: we are to be visited by the two kids just described, at least one of which is a girl. It’s a matter of chance who arrives first. The first child enters — a girl. The second knocks. What are the odds it’s a boy? Answer: 1 in 2. Paradoxical but true. (Thanks to Len Ragozin of New York City.)

Cecil is happy to say he has heard from the originator of the Monty Hall question, Steve Selvin, a UCal-Berkeley prof (cf American Statistician, February 1975). Cecil is happy because he can now track Steve down and have him assassinated, as he richly deserves for all the grief he has caused. Hey, just kidding, doc. But next time you have a brainstorm, do us a favor and keep it to yourself.

I'm a pilot and I work for an aircraft manufacturing company. Just like every other pilot and many non-pilots, I've learned that aircraft fly because of the low pressure created on the top of an airfoil. However, I'm not sure that's the whole story. I recently read a book called Stick and Rudder by Wolfgang Langewiesche, and he argues that the primary thing that keeps planes in the air is the downward force created by the wing--that the aircraft mostly pushes itself into the sky instead of pulling itself by the top of the wings. I've been thinking (perhaps too much) that he may be right. Perhaps lift is created by both effects. Maybe one is stronger than the other but I think that most people haven't been told the real story about what keeps an airplane in the air. It's got to be more than the low pressure on top of the wing. I want to know the real story.

Bill Rehm

aerodave replies:

You’d think that after a century of powered flight we’d have this lift thing figured out. Unfortunately, it’s not as clear as we’d like. A lot of half-baked theories attempt to explain why airplanes fly. All try to take the mysterious world of aerodynamics and distill it into something comprehensible to the lay audience–not an easy task. Nearly all of the common "theories" are misleading at best, and usually flat-out wrong.

You mention a couple concepts that provide part of the answer but are incomplete in fundamental ways. To hear some tell it, wings work due to angle of attack and little else. Angle of attack (AOA) is the difference between the orientation of a surface and the direction of the air flowing over it. If you hold your hand horizontally out the window of a moving car, and then start to point your fingers toward the sky, you’re giving your hand a positive AOA. That generates a significant amount of upward force on your arm. It makes sense that this same force should keep a plane in the air, and to some degree it does. A wing’s angle of attack helps it deflect air downward, and Newton’s Third Law–every action has an equal and opposite reaction–says this downward push on the air must result in an upward push on the wing. But there’s more to it, since the force generated by this deflection alone is far short of what we see in real life.

The problem is that the AOA explanation ignores the cross-sectional shape of the wing–the quintessential aerodynamic form known as the airfoil. In particular, it suggests that it doesn’t matter how the top of the wing is shaped, and that a thin flat plate would do just fine. Not so. Cambered airfoils–those with the characteristic upward hump that most wings have–can generate lift without any positive AOA at all, or even a slightly negative angle!

Of all the flawed explanations of why planes fly, the one most people have heard involves the Bernoulli principle and "equal transit times." The curved upper surface of the wing is longer than the bottom one, we’re told, and the air above the wing must therefore speed up to keep pace with its counterpart below. Start with this increased velocity on the top of the wing, mix in Bernoulli’s principle, and you find lower pressure above. This pressure differential sucks the airplane upward and voilà! A quarter-million pounds of jumbo jet stays aloft.

This logic is taught to students of all ages, and finds its way into many respectable science textbooks. Its only problem is its complete lack of resemblance to reality. A given "piece" of upper-surface air has no compelling reason to keep pace with its estranged sibling below; it can’t know and doesn’t care what’s happening on the other side of that aluminum partition.

That’s not to say this model totally misses the mark; it just underestimates the effect. The air really does accelerate over the top of the wing, but actually far outpaces the lower-surface air. It’s a good thing, too–if the air stayed in sync over the minuscule difference between the upper and lower paths, a Cessna 152 would have to fly at over 300 mph just to stay in the air! (In reality, it’s about 55 mph.)

By this point I’m sure you’re tired of hearing all the non-reasons airplanes fly and would like a real answer. Where does lift come from? One important fact is that fluids have a tendency to adhere to curved surfaces as they flow past. This is called the Coanda effect. The explanation for it is outside the scope of this article, so you’ll have to take my word for it or check out the references. The bottom line is that if you correctly shape the top of the wing, the air will keep hugging the surface as it passes.

The next step is realizing that when a fluid is made to curve, its pressure is "thrown" to the outside by centrifugal force (that’s the simplest way of describing it). As the air crests the hill at the top of the airfoil, it pulls away from the wing surface, creating a slight vacuum next to the metal. The pressure differential helps push the wing up. In addition, the wing causes the flow behind it to move downward. Some of the downward flow is caused by air deflected by the lower surface, and some comes from air that is forced down as it rounds the top. (That’s where the missing lift we mentioned in connection with the AOA explanation comes from!) In short, an airfoil generates lift up by deflecting the air flow down, a clear example of Newton’s Third Law. This illustration makes the notion of downward deflection a little clearer.

Is it wrong to invoke the Bernoulli principle when explaining how an airfoil works? No, but it tends to confuse matters for the non-technical audience. In fact, airfoils can be explained in two ways. I’ve just given the "Newton" explanation–a wing generates lift because it deflects the airflow. The "Bernoulli" explanation has to do with pressure differentials. For complex reasons we needn’t get into (other than to say they have little to do with equal transit times), air moves faster over the top of a wing than beneath it. Bernoulli’s principle tells us that the higher the velocity of an airstream, the lower its static pressure. Because the static pressure below the wing is higher than that above, the wing generates lift. If you don’t quite follow all that, don’t worry–the Newton explanation is perfectly adequate.

That’s the simple explanation of lift. Using that knowledge to design anything useful is a little messier. There’s a big set of equations that in principle can be solved to fully describe the behavior of a moving fluid. They’re called the Navier-Stokes equations, and they’ve got more Greek letters than the Athens phone book. (Check out this page to see what I mean.) When applied to anything approaching reality, they get so hairy they gag the world’s fastest computers. So engineers make lots of simplifying assumptions to produce results that are "good enough." That’s why we have a hard time predicting how real bodies will behave, and why experimentation is so important in aeronautics.

How can aviation be grounded in such a muddy understanding of the underlying physics? As with many other scientific phenomena, it’s not always necessary to understand why something works to make use of it. We engineers are happy if we’ve got enough practical knowledge to build flying aircraft. The rest we chalk up to magic.

Further reading:

Gale M. Craig’s 2002 book Introduction to Aerodynamics does an excellent job of breaking down the misconceptions of flight and explaining the reality with enough math for the techies, but plenty of great description for the non-engineer.

STAFF REPORTS ARE WRITTEN BY THE STRAIGHT DOPE SCIENCE ADVISORY BOARD, CECIL'S ONLINE AUXILIARY. THOUGH THE SDSAB DOES ITS BEST, THESE COLUMNS ARE EDITED BY ED ZOTTI, NOT CECIL, SO ACCURACYWISE YOU'D BETTER KEEP YOUR FINGERS CROSSED.

Scientifically speaking, is music universal? If some advanced extraterrestrial came to earth, would he recognize our music?

Jim B., via the Straight Dope Message Board

Cecil replies:

Is music universal? Well, that’s a bet being made by the group Messaging Extraterrestrial Intelligence. Not content to simply scan the skies for signs of life, the METI folks want to go ahead and say howdy, which they’re attempting to do via a transmission station in Norway, beaming a binary-coded message at one potentially life-friendly exoplanet 12 light-years away. The content of their message? Melodies, created in collaboration with an artsy Barcelona music festival — lest you thought we’d subject our pen pals to, say, “Escape (The Pina Colada Song).”

For the moment, let’s put the more, uh, universal sense of “universal” on hold and start a little closer to home. Leaving aside all the pop-sci baloney about music being a “universal language” — a phrase specially calibrated to drive both musicologists and linguists nuts — we can say nonetheless that music is universal here on earth: virtually all cultures produce it in some form. We’ve been at it a long time, creating tunes for at least 50,000 years — possibly as long as 250,000, if you count our a cappella period.

This long-term commitment has led some scientists to suggest that the tendency to make music must have had some role to play natural-selection-wise. But what? The list of theories is longer than Wagner’s Ring Cycle: music could have been a “proto-language,” a mode of human communication before formal languages developed; music might facilitate social cohesion, like grooming does for other primates; music might soothe cognitive dissonance in our brains and help us perform complex tasks; and so on.

Not exactly settled science, but let’s accept for the sake of discussion that our taste for music is an evolutionary adaptation. Is there any reason to think our friends from the exoplanet GJ 273b — the target audience for the METI transmission — would’ve evolved similarly? I’ll point you toward an intriguing recent paper in the International Journal of Astrobiology, where a few scientists argue that if advanced extraterrestrials have also undergone a process of natural selection (and there’s no reason to think otherwise), they might resemble us in some fundamental biological ways, and to a degree that might surprise us.

But can they boogie? I regret to inform you this paper didn’t go so far as to venture a guess, Jim. It’s not too hard, though, to make the case it shouldn’t matter either way.

Besides the musical passages, the METI message contains a primer on earth math and physics — from basic arithmetic and geometry up through trig, which gets you to the sine function and ultimately to the wave forms that convey audible sound, as well as a clock function meant to get across the idea of measuring time in seconds. The plan is to provide a conceptual toolkit for budding music lovers on other planets: everything they’d need, ideally, to look at the other data and have a shot at figuring out it’s supposed to represent notes at various pitches over varying lengths of time.

Even if the aliens can’t hear the music in the sense that we understand hearing, they’ll be able to perceive the patterns formed by its constituent data, and, with any luck, grok it anyway. The mathematical orderliness of Bach’s Goldberg Variations, you’d think, might have a beauty that transcends mere audibility. And who knows? Maybe the receiving civilization will have some souped-up hi-fi equipment that transposes our sound waves into a spectrum more locally popular — light, say.

Just the same, they may not see what the big deal is. In a 2001 paper, the musicologist David Huron asks us, in the service of explaining various evolutionary theories of music, to engage in a little thought experiment. Imagine you’re an alien scientist visiting earth, Huron writes. A lot of what you see makes sense to you on a behavioral level: eating, sleeping, etc. But you’d also see us creating music, listening to it, incorporating it into our religious ceremonies and mating rituals — and all this you might find yourself baffled by. “Even if Martian anthropologists had ears, I suspect they would be stumped by music,” Huron concludes.

His point is that music as we understand it may be a uniquely human behavior — graspable by extraterrestrial listeners, sure, but they might find our devotion curious. To be fair, this wouldn’t put them too far behind earth anthropologists; as discussed earlier, we’re still puzzling it out ourselves.

From METI’s perspective, this isn’t a bug but a feature: any alien civilization we contact, the thinking goes, is likely to be much more advanced than we are, so bragging about our scientific achievements is probably pointless — they’re there already, whereas music and other earthly arts might be sui generis enough to pique their interest. To me, though, this argues for sending the very best stuff we’ve got. No offense to the composers in Barcelona, but if we’re trying to turn extraterrestrial heads here, why screw around? Play ’em some Stevie Wonder already.

It’s the price you pay for your more complex cellular organization. The downside is that if you get an arm cut off, you can’t regrow it. But the bright side is you don’t have to live your life in a mud flat eating plankton.

The issue here isn’t so much what other organisms have that we don’t, but rather what we have LOST that just about everything else has always had. The capacity for regeneration is a matter of cellular recognition during development. A good parallel is the comparison between, say, a pack of wolves and a termite colony. In a pack of wolves, one’s identity and relationship to other pack members are flexible things. You can be the alpha male one day, and kicked out of the pack the next (though a male wolf will not suddenly turn into a female wolf, so there ARE limits). In a termite, once you reach adulthood as a queen/king, you are STUCK.

This same sort of interaction takes place in most organisms at the cellular level. In many organisms, cellular identity has a certain degree of flexibility, and what a given cell turns into depends on what its neighbors are. But there are often restrictions built into this, tending to become more restrictive as an organism becomes more complex. So, just as a termite MAY be able to switch from worker to queen if the switch occurs before adulthood, but loses that ability later, some organisms lose the capacity to regenerate once they’re past a certainly developmental stage. Humans fall into that category. If a newborn baby loses a fingertip, it will regenerate; if a 30-year-old loses a fingertip, that’s that.

What it comes down to is that when an organism is wounded, depending on which type of tissue is involved at the wound site, the repair mechanism may or may not involve cells that still have flexibility in their “programming.” If the cells are still flexible, then they act like they might in an embryo; check what your neighbor cells are, and adjust accordingly. It’s like having a big blueprint that only tells you what goes next to what–you can rebuild a limb or organ that way as long as the cells have some sort of orientation info available (which way is up, where the head/tail is, etc.). Such cells will keep budding off new cells until the plan in the blueprint is completed. If the cells are NOT flexible, as in most adult vertebrates, then when the repair occurs, the damage is filled in with tissue lacking much identity, and which doesn’t produce new cells: scar tissue.

To finish the story, some vertebrates can regenerate portions of their anatomy after reaching adulthood, most notably amphibians (salamanders especially; that they should retain such abilities is not surprising when you consider that amphibians undergo metamorphosis, so their cells HAVE TO retain flexibility), and some snakes and lizards that can regrow tails. Not us humans. If we have cells that lose their identity and start to proliferate, we call them “cancer.”

Why are processed foods bad? If I take a chicken breast and process it into a paste, is it worse for my health than if I ate the chicken whole? Please help before I get butt cancer from a chicken nugget!

Jim Huff

Cecil replies:

Let’s get the bad news out of the way, Jim. Last month a big French study came out that tracked the diets of some 100,000 participants to better understand the relationship between cancer and what its authors refer to as “ultra-processed foods,” characterized by “a higher content of total fat, saturated fat, and added sugar and salt, along with a lower fibre and vitamin density.” And though butt cancer wasn’t named as a specific threat, the findings did in fact link a 10 percent proportional increase in consumption of such food with a 10 percent-plus rise in cancer risk overall. Further research is needed, but — brace yourselff — it’s looking like chicken nuggets may not be amazing for your health.

The good news? Your skepticism regarding any categorical condemnation of “processed foods” is entirely warranted. This reality, in fact, is a big part of the organizing principle underlying the French research — about which more below. Not only is there nothing inherently bad about processed foods, the phrase itself is so capacious and variously defined as to be basically meaningless. Unless you’re picking grapes off the vine, you’re eating food that’s been processed somehow or other: milk is pasteurized; wheat is ground; salad mix is washed. A 2000 article in the British Medical Bulletin defined food processing as “any procedure undergone by food commodities after they have left the primary producer, and before they reach the consumer” — mere refrigeration counts.

That’s a distinctly capitalist formulation, but by most definitions, humans have engaged in food processing for millennia. Cooking with fire is the ur-processing method, and our ancestors may have been at it 1.5 million years ago. Other techniques have involved creative ways to unlock nutrition in food or extend its shelf life. In the former category, see e.g. nixtamalization, the practice of treating maize with limestone or lye, which helped the Aztecs and Mayans get more protein and disease-preventing vitamins in their diet. For the latter, see basically any form of fermentation: milk turned into cheese and yogurt is the most widespread, but you’ve also got Korean kimchi (fermented vegetables), Nigerian ogi (fermented grains), and assorted smelly preserved-fish dishes encountered at high latitudes, including Swedish surströmming, Norwegian rakfisk, and “stinkheads,” which the Yupik people of Alaska prepare by burying salmon heads in the ground and leaving them to age.

Many methods of fermenting, curing, etc. rely on salt — an extremely consequential ingredient in this realm, particularly prior to refrigeration. But salt took its own place among processed foods early in the 20th century when we began fortifying it with iodine, essential for thyroid function. In coastal regions, iodine in the soil makes its way into the groundwater, but further inland you won’t find enough of it occurring naturally, and till the 1920s there was a huge swath of the northern U.S., stretching from the Appalachians to the Cascades — the “goiter belt,” they called it — where between a quarter and 70 percent of all kids displayed visibly enlarged thyroids. Just as adding vitamin D to milk took care of our national rickets problem, iodized salt pretty much wiped out goiter, plus some serious developmental disorders also associated with iodine deficiency. It’s been floated as one factor behind what’s known as the Flynn effect: the three-point-per-decade rise in IQ observed in developed countries over the 20th century.

So yeah, food processing has done a thing or two for humanity. We haven’t even touched on the fact that urbanization would have been a hell of a lot harder without food preserved for shipping from the hinterlands, or that the zillion hours of food-prep labor we’ve saved by not making everything from scratch would have fallen disproportionately on women’s shoulders.

Do “processed foods,” then, deserve their bad rap? Answer: no, which is something public-health experts are coming around on. The French study discussed above uses a four-category food-classification system proposed by Brazilian researchers in 2010 that separates harmless or beneficial food processing from the problematic sort. NOVA, as the scheme’s called, distinguishes between unprocessed or minimally processed foods (e.g. meats, plants); processed culinary ingredients (sugar, vegetable oils); processed foods (canned vegetables, cured meats); and, finally, ultra-processed foods, defined as “industrial formulations with five or more and usually many ingredients,” including “substances not commonly used in culinary preparations.”

And yes, the NOVA authors list “poultry and fish ‘nuggets’” in this last group. Again, one thing typifying ultra-processed foods is low nutrient density and high energy density, what with all that added fat and carbs. Those traits are much of (a) the real problem, as far as healthy eating goes, and (b) why Doritos taste so good. But I hope by now you’re distinguishing this kind of stuff from your homemade chicken paste, which isn’t the kind of processed food you need to worry about. Appealing as it sounds, though, I’m afraid I’ve got dinner plans.

An engineering professor used to tell our class, "Everything eventually fails. The question is, when?" So what happens with a mammoth building? What's the intended life span of, say, the Willis Tower? The way cities are packed, I can't imagine a demolition crew can just drop a hundred-story building without causing chaos.

Concerned Citizen in Chicago

Cecil replies:

I’ll concede that “Everything eventually fails” is more than useful enough as credos go. But there’s a power at work here that can give even the ravages of time a fair fight: the profit motive. Last winter, the owners of the Willis Tower announced a $500 million plan to modernize the 45-year-old building, and the city started issuing permits over the summer. Clearly somebody doesn’t think that thing’s coming down anytime soon.

Renovating and retrofitting is increasingly the name of the game when it comes to giant buildings, the current thinking being that it’s financially (not to mention ecologically) smarter to refresh them periodically than to tear down and start anew. Most experts figure there’s no reason an appropriately upkept skyscraper can’t stay there pretty much indefinitely.

Without upkeep? As we discussed in a 2016 column, towers in a low-lying city like New York, for instance, would have only about 50 years of life in them absent human intervention: water erodes foundations if no one’s around to continually pump it out. In general, if you want to keep a structure standing, you’re going to need a sound water-management plan; foundation aside, one requirement for skyscraper longevity is that their steel-reinforced concrete bones don’t get exposed to rain, the acid in which eats at the limestone content.

But assuming they get proper TLC, the dinosaurs of the Manhattan skyline will likely hang around a while yet. Sure, we can expect to lose a few old office towers here and there in the coming decades, mainly structures that were built when energy was cheap and nowadays cost a fortune to heat and cool — all that single-pane glass, etc. But by and large in New York, market forces and building code collude to keep old buildings standing. Many skyscrapers went up in an era of fewer regulatory constraints, so developers thinking about a tear-down today may be looking at a necessarily smaller building in its place — and thus less rent revenue going forward.

Now, Tokyo is another story. Owing to the local mix of property values, zoning laws, and design standards, it often makes more sense there to knock down and rebuild. As the New York Times put it a couple of years ago, there’s a bull market for demolition in Japan, and the nation is becoming a world leader in the fine art of removing skyscrapers.

The fine art? I’m guessing when you’re picturing the “chaos” of skyscraper demolition, CCC, you’re investing the scene with a lot of unwarranted drama — dynamite, countdown, plunger-style detonator, great clouds of dust and debris. In fact, the implosion method is now used for only about 2 percent of demolitions; most buildings, particularly in dense urban areas, are taken apart more laboriously, using cranes and elbow grease.

Those in the deconstruction business are constantly coming up with new techniques, though, and right now is a particularly exciting time to be a building wrecker. In South Africa, they’re using high-pressure gas canisters in place of dynamite to break up concrete — quieter, less violent, and a lot less permitting required. In France, remote-controlled hydraulic devices push over supporting walls on midlevel floors, causing the top of the building to cave in on itself and pancake the rest on its way down.

But the Japanese are out ahead of the pack. They’ve got lots of buildings to practice on, many just too tall and too tightly surrounded to raze the old-fashioned way, and since 2002 they’ve been bound by a stringent law mandating the reuse of building materials, encouraging them to make as little mess as possible. As such, Japanese companies have worked up startlingly gentle demolition techniques — you can find trippy time-lapse videos where structures appear to just slowly sink into the ground. In one method, the roof is held up by jacks as workers remove the top floor in its entirety; the roof is then lowered, and the process continues until the building’s disappeared. Employing a similar concept, another version starts from the bottom: workers jack up everything above the ground floor, then take that out; rinse, repeat.

Fancy, and not just on the safety front: these demolition firms boast that their recycling of materials and relatively modest use of heavy machinery leads to impressive reductions in carbon emissions — up to 85 percent in some cases. Plus, the whole deal looks about as quiet and smooth-running as the Tokyo subway. There’s no indication such techniques will make it to New York or Chicago in the near future, but neither will the incentives to demolish in the first place. Nor will notably quiet and smooth-running subways, for that matter. In more ways than one, we’re stuck with the cities we’ve got.

WASHINGTON - The center of our galaxy is teeming with black holes, sort of like a Times Square for strange super gravity objects, astronomers discovered.

For decades, scientists theorized that circling in the center of galaxies, including ours, were lots of stellar black holes , collapsed giant stars where the gravity is so strong even light doesn’t get out. But they hadn’t seen evidence of them in the Milky Way core until now.

Astronomers poring over old x-ray observations have found signs of a dozen black holes in the inner circle of the Milky Way. And since most black holes can’t even be spotted that way, they calculate that there are likely thousands of them there. They estimate it could be about 10,000, maybe more, according to a study in Wednesday’s journal Nature .

“There’s lots of action going on there,” said study lead author Chuck Hailey, a Columbia University astrophysicist. “The galactic center is a strange place. That’s why people like to study it.”

The stellar black holes are in addition to — and essentially circling — the already known supermassive black hole, called Sagittarius A , that’s parked at the center of the Milky Way.

In the rest of the massive Milky Way, scientists have only spotted about five dozen black holes so far, Hailey said.

The newly discovered black holes are within about 19.2 trillion miles (30.9 trillion kilometers) of the supermassive black hole at the center. So there’s still a lot of empty space and gas amid all those black holes. But if you took the equivalent space around Earth there would be zero black holes, not thousands, Hailey said.

Earth is in spiral arm around 3,000 light years away from the center of the galaxy. (A light year is 5.9 trillion miles, or 9.5 trillion kilometers.)

Harvard astronomer Avi Loeb, who wasn’t part of the study, praised the finding as exciting but confirming what scientists had long expected.

The newly confirmed black holes are about 10 times the mass of our sun, as opposed to the central supermassive black hole, which has the mass of 4 million suns. Also the ones spotted are only the type that are binary , where a black hole has partnered with another star and together they emit large amount of x-rays as the star’s outer layer is sucked into the black hole. Those x-rays are what astronomers observe.

When astronomers look at closer binary black hole systems they could then see the ratio between what’s visible and what’s too faint to be observed from far away. Using that ratio, Hailey figures that even though they only spotted a dozen there must be 300 to 500 binary black hole systems.

But binary black hole systems are likely only 5 percent of all black holes, so that means there are really thousands of them, Hailey said.

There are good reasons the Milky Way’s black holes tend to be in the center of the galaxy, Hailey said.

First, their mass tends to pull them to the center. But mostly the center of the galaxy is the perfect “hot house” for black hole formation, with lots of dust and gas.

Hailey said it is “sort of like a little farm where you have all the right conditions to produce and hold on to a large number of black holes.”

On June 17, the political commentator Ann Coulter, appearing as a guest on Fox News, asserted that crying migrant children separated from their parents are “child actors.” Does this groundless claim deserve as much airtime as, for example, a historically informed argument from Ta-Nehisi Coates that structural racism makes the American dream possible?

Jordan Peterson, a professor of psychology at the University of Toronto, has complained that men can’t “control crazy women” because men “have absolutely no respect” for someone they cannot physically fight. Does this adolescent opinion deserve as much of an audience as the nuanced thoughts of Kate Manne, a professor of philosophy at Cornell University, about the role of “himpathy” in supporting misogyny?

We may feel certain that Coulter and Peterson are wrong, but some people feel the same way about Coates and Manne. And everyone once felt certain that the Earth was the center of the solar system. Even if Coulter and Peterson are wrong, won’t we have a deeper understanding of why racism and sexism are mistaken if we have to think for ourselves about their claims? And “who’s to say” that there isn’t some small fragment of truth in what they say?

If this specious line of thought seems at all plausible to you, it is because of the influence of “On Liberty,” published in 1859 by the English philosopher John Stuart Mill. Mill’s argument for near-absolute freedom of speech is seductively simple. Any given opinion that someone expresses is either wholly true, partly true or false.

To claim that an unpopular or offensive opinion cannot be true “is to assume our own infallibility.” And if an offensive opinion is true, to limit its expression is clearly bad for society. If an opinion is partly true, we should listen to it, because “it is only by the collision of adverse opinions, that the remainder of the truth has any chance of being supplied.” And even if an opinion is false, society will benefit by examining the reasons it is false. Unless a true view is challenged, we will hold it merely “in the manner of a prejudice, with little comprehension or feeling of its rational grounds.”

The problem with Mill’s argument is that he takes for granted a naïve conception of rationality that he inherited from Enlightenment thinkers like René Descartes. For such philosophers, there is one ahistorical rational method for discovering truth, and humans (properly educated) are approximately equal in their capacity for appreciating these truths. We know that “of all things, good sense is the most fairly distributed,” Descartes assures us, because “even those who are the hardest to satisfy in every other respect never desire more of it than they already have.”

Of course, Mill and Descartes disagreed fundamentally about what the one ahistorical rational method is — which is one of the reasons for doubting the Enlightenment dogma that there is such a method.

If you do have faith in a universal method of reasoning that everyone accepts, then the Millian defense of absolute free speech is sound. What harm is there in people hearing obvious falsehoods and specious argumentation if any sane and minimally educated person can see through them? The problem, though, is that humans are not rational in the way Mill assumes. I wish it were self-evident to everyone that we should not discriminate against people based on their sexual orientation, but the current vice president of the United States does not agree. I wish everyone knew that it is irrational to deny the evidence that there was a mass shooting in Sandy Hook, but a syndicated radio talk show host can make a career out of arguing for the contrary.

Historically, Millian arguments have had some good practical effects. Mill followed Alexis de Tocqueville in identifying “the tyranny of the majority” as an ever-present danger in democracies. As an advocate of women’s rights and an opponent of slavery, Mill knew that many people then regarded even the discussion of these issues as offensive. He hoped that by making freedom of speech a near absolute right he could guarantee a hearing for opinions that were true but unpopular among most of his contemporaries.

However, our situation is very different from that of Mill. We are seeing the worsening of a trend that the 20th century German-American philosopher Herbert Marcuse warned of back in 1965: “In endlessly dragging debates over the media, the stupid opinion is treated with the same respect as the intelligent one, the misinformed may talk as long as the informed, and propaganda rides along with education, truth with falsehood.” This form of “free speech,” ironically, supports the tyranny of the majority.

The media are motivated primarily by getting the largest audience possible. This leads to a skewed conception about which controversial perspectives deserve airtime, and what “both sides” of an issue are. How often do you see controversial but well-informed intellectuals like Noam Chomsky and Martha Nussbaum on television? Meanwhile, the former child-star Kirk Cameron appears on television to explain that we should not believe in evolutionary theory unless biologists can produce a “crocoduck” as evidence. No wonder we are experiencing what Marcuse described as “the systematic moronization of children and adults alike by publicity and propaganda.”

Marcuse was insightful in diagnosing the problems, but part of the solution he advocated was suppressing right-wing perspectives. I believe that this is immoral (in part because it would be impossible to do without the exercise of terror) and impractical (given that the internet was actually invented to provide an unblockable information network). Instead, I suggest that we could take a big step forward by distinguishing free speech from just access. Access to the general public, granted by institutions like television networks, newspapers, magazines, and university lectures, is a finite resource. Justice requires that, like any finite good, institutional access should be apportioned based on merit and on what benefits the community as a whole.

There is a clear line between censoring someone and refusing to provide them with institutional resources for disseminating their ideas. When Nathaniel Abraham was fired in 2004 from his position at Woods Hole Oceanographic Institute because he admitted to his employer that he did not believe in evolution, it was not a case of censorship of an unpopular opinion. Abraham thinks that he knows better than other scientists (and better than other Christians, like Pope Francis, who reminded the faithful that God is not “a magician, with a magic wand”). Abraham has every right to express his ignorant opinion to any audience that is credulous enough to listen. However, Abraham does not have a right to a share of the intellectual capital that comes from being associated with a prestigious scientific institution like Woods Hole.

Similarly, the top colleges and universities that invite Charles Murray to share his junk science defenses of innate racial differences in intelligence (including Columbia and New York University) are not promoting fair and balanced discourse. For these prestigious institutions to deny Murray an audience would be for them to exercise their fiduciary responsibility as the gatekeepers of rational discourse. We have actually seen a good illustration of what I mean by “just access” in ABC’s courageous decision to cancel “Roseanne,” its highest-rated show. Starring on a television show is a privilege, not a right. Roseanne compared a black person to an ape. Allowing a show named after her to remain on the air would not be impartiality; it would be tacitly endorsing the racist fantasy that her views are part of reasonable mainstream debate.

Donald Trump, first as candidate and now as president, is such a significant news story that responsible journalists must report on him. But this does not mean that he should be allowed to set the terms of the debate. Research shows that repeatedly hearing assertions increases the likelihood of belief — even when the assertions are explicitly identified as false. Consequently, when journalists repeat Trump’s repeated lies, they are actually increasing the probability that people will believe them.

Even when journalistic responsibility requires reporting Trump’s views, this does not entail giving all of his spokespeople an audience. MSNBC’s “Morning Joe,” set a good precedent for just access by banning from the show Kellyanne Conway for casually spouting “alternative facts.”

Marcuse also suggested, ominously, that we should not “renounce a priori violence against violence.” Like most Americans, I spontaneously cheered when I saw the white nationalist Richard Spencer punched in the face during an interview. However, as I have noted elsewhere, Mahatma Gandhi and the Rev. Martin Luther King, Jr. showed us that nonviolent protest is not only a moral demand (although it is that too); it is the highest strategic cunning. Violence plays into the hands of our opponents, who relish the opportunity to play at being martyrs. Consequently, while it was wrong for Middlebury College to invite Murray to speak, it was even more wrong for students to assault Murray and a professor escorting him across campus. (Ironically, the professor who was injured in this incident is a critic of Murray who gave a Millian defense of allowing him to speak on campus.)

What just access means in terms of positive policy is that institutions that are the gatekeepers to the public have a fiduciary responsibility to award access based on the merit of ideas and thinkers. To award space in a campus lecture hall to someone like Peterson who says that feminists “have an unconscious wish for brutal male domination,” or to give time on a television news show to someone like Coulter who asserts that in an ideal world all Americans would convert to Christianity, or to interview a D-list actor like Jenny McCarthy about her view that actual scientists are wrong about the public health benefits of vaccines is not to display admirable intellectual open-mindedness. It is to take a positive stand that these views are within the realm of defensible rational discourse, and that these people are worth taking seriously as thinkers.

Neither is true: These views are specious, and those who espouse them are, at best, ignorant, at worst, sophists. The invincibly ignorant and the intellectual huckster have every right to express their opinions, but their right to free speech is not the right to an audience.

Bryan W. Van Norden is a professor of philosophy at Wuhan University, Yale-NUS College and Vassar College. He is the author, most recently, of “Taking Back Philosophy: A Multicultural Manifesto.”

It’s a tough time to defend religion. Respect for it has diminished in almost every corner of modern life — not just among atheists and intellectuals, but among the wider public, too. And the next generation of young people looks likely to be the most religiously unaffiliated demographic in recent memory.

There are good reasons for this discontent: continued revelations of abuse by priests and clerics, jihad campaigns against “infidels” and homegrown Christian hostility toward diversity and secular culture. This convergence of bad behavior and bad press has led many to echo the evolutionary biologist E. O. Wilson’s claim that “for the sake of human progress, the best thing we could possibly do would be to diminish, to the point of eliminating, religious faiths.”

Despite the very real problems with religion — and my own historical skepticism toward it — I don’t subscribe to that view. I would like to argue here, in fact, that we still need religion. Perhaps a story is a good way to begin.

One day, after pompously lecturing a class of undergraduates about the incoherence of monotheism, I was approached by a shy student. He nervously stuttered through a heartbreaking story, one that slowly unraveled my own convictions and assumptions about religion.

Five years ago, he explained, his older teenage brother had been brutally stabbed to death, viciously attacked and mutilated by a perpetrator who was never caught. My student, his mother and his sister were shattered. His mother suffered a mental breakdown soon afterward and would have been institutionalized if not for the fact that she expected to see her slain son again, to be reunited with him in the afterlife where she was certain his body would be made whole. These bolstering beliefs, along with the church rituals she engaged in after her son’s murder, dragged her back from the brink of debilitating sorrow, and gave her the strength to continue raising her other two children — my student and his sister.

To the typical atheist, all this looks irrational, and therefore unacceptable. Beliefs, we are told, must be aligned with evidence, not mere yearning. Without rational standards, like those entrenched in science, we will all slouch toward chaos and end up in pre-Enlightenment darkness.

I do not intend to try to rescue religion as reasonable. It isn’t terribly reasonable. But I do want to argue that its irrationality does not render it unacceptable, valueless or cowardly. Its irrationality may even be the source of its power.

The human brain is a kludge of different operating systems: the ancient reptilian brain (motor functions, fight-or-flight instincts), the limbic or mammalian brain (emotions) and the more recently evolved neocortex (rationality). Religion irritates the rational brain because it trades in magical thinking and no proof, but it nourishes the emotional brain because it calms fears, answers to yearnings and strengthens feelings of loyalty.

According to prominent neuroscientists like Jaak Panksepp, Antonio Damasio and Kent Berridge, as well as neuropsychoanalysts like Mark Solms, our minds are motivated primarily by ancient emotional systems, like fear, rage, lust, love and grief. These forces are adaptive and help us survive if they are managed properly — that is if they are made strong enough to accomplish goals of survival, but not so strong as to overpower us and lead to neuroses and maladaptive behavior.

My claim is that religion can provide direct access to this emotional life in ways that science does not. Yes, science can give us emotional feelings of wonder at the majesty of nature, but there are many forms of human suffering that are beyond the reach of any scientific alleviation. Different emotional stresses require different kinds of rescue. Unlike previous secular tributes to religion that praise its ethical and civilizing function, I think we need religion because it is a road-tested form of emotional management.

Of course, there is a well-documented dark side to spiritual emotions. Religious emotional life tilts toward the melodramatic. Religion still trades readily in good-and-evil narratives, and it gives purchase to testosterone-fueled revenge fantasies and aggression. While this sort of zealotry is undeniably dangerous, most religion is actually helpful to the average family struggling to eke out a living in trying times.

Religious rituals, for example, surround the bereaved person with our most important resource — other people. Even more than other mammals, humans are extremely dependent on others — not just for acquiring resources and skills, but for feeling well. And feeling well is more important than thinking well for my survival.

Religious practice is a form of social interaction that can improve psychological health. When you’ve lost a loved one, religion provides a therapeutic framework of rituals and beliefs that produce the oxytocin, internal opioids, dopamine and other positive affects that can help with coping and surviving. Beliefs play a role, but they are not the primary mechanisms for delivering such therapeutic power. Instead, religious practice (rituals, devotional activities, songs, prayer and story) manage our emotions, giving us opportunities to express care for each other in grief, providing us with the alleviation of stress and anxiety, or giving us direction and an outlet for rage.

Atheists like Richard Dawkins, E. O. Wilson and Sam Harris, are evaluating religion at the neocortical level — their criteria for assessing it is the rational scientific method. I agree with them that religion fails miserably at the bar of rational validity, but we’re at the wrong bar. The older reptilian brain, built by natural selection for solving survival challenges, was not built for rationality. Emotions like fear, love, rage — even hope or anticipation — were selected for because they helped early mammals flourish. In many cases, emotions offer quicker ways to solve problems than deliberative cognition.

For us humans, the interesting issue is how the old animal operating system interacts with the new operating system of cognition. How do our feelings and our thoughts blend together to compose our mental lives and our behaviors? The neuroscientist Antonio Damasio has shown that emotions saturate even the seemingly pure information-processing aspects of rational deliberation. So something complicated is happening when my student’s mother remembers and projects her deceased son, and embeds him in a religious narrative that helps her soldier on.

No amount of scientific explanation or sociopolitical theorizing is going to console the mother of the stabbed boy. Bill Nye the Science Guy and Neil deGrasse Tyson will not be much help, should they decide to drop over and explain the physiology of suffering and the sociology of crime. But the magical thinking that she is going to see her murdered son again, along with the hugs from and songs with fellow parishioners, can sustain her. If this emotionally grounded hope gives her the energy and vitality to continue caring for her other children, it can do the same for others. And we can see why religion persists.

Those of us in the secular world who critique such emotional responses and strategies with the refrain, “But is it true?” are missing the point. Most religious beliefs are not true. But here’s the crux. The emotional brain doesn’t care. It doesn’t operate on the grounds of true and false. Emotions are not true or false. Even a terrible fear inside a dream is still a terrible fear. This means that the criteria for measuring a healthy theory are not the criteria for measuring a healthy emotion. Unlike a healthy theory, which must correspond with empirical facts, a healthy emotion is one that contributes to neurochemical homeostasis or other affective states that promote biological flourishing.